The rate of change is dy/dx =4.
The rate of change, often represented as dy/dx or the derivative, expresses how one variable changes concerning another. In this scenario, as the x value increases by 3, and the y value increases by 12, the rate of change can be calculated by dividing the change in y (Δy) by the change in x (Δx).
In mathematical terms, the rate of change is given by the formula dy/dx = Δy/Δx. Here, dy/dx =12/3=4. Therefore, the rate of change is 4, indicating that for every increase of 3 in the x value, the y value increases by 12, maintaining a constant ratio of 4:1. This rate of change signifies the linear relationship between the variables x and y in the given context.